Step-by-step explanation:
I assume the measuring cylinder measures the cm³ of its normally liquid content.
because for anything else we would need more information about the dimensions of the cylinder.
and so, originally the cylinder shows 40 cm³.
after dropping the stone in, how many cm³ of water is the cylinder then showing ?
let's first mention some facts we are going to use :
water weighs 1 kg (1000 g) per liter.
and 1 liter fits exactly into a cube of
10 cm × 10 cm × 10 cm = 1000 cm³
so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.
the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).
how many cm³ does the stone have (and replaces water) ?
well, it has 129 g, and 8.6 g of the stone fill a cm³.
so, it has
129 / 8.6 = 15 cm³
therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.
and the cylinder reads now 55 cm³.
FYI : but there is still only 40 cm³ of water in there.
this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).
Answer: 55 cm³.
Step-by-step explanation:
[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]
PLS HELP IM STUCK PLS
Answer:
-4
Step-by-step explanation:
We are going to substitute 0 in for x and solve for y.
-2(0)+ 8y = -32 Anything times zero is zero
0 + 8 y = -32 Anything plus zero is itself.
8y = -32 Divide both sides by 8
y = -4
The real solutions to the quadratic -x² - 2x+5=0 are:
2± √√29
2
-1±-√6
No real solutions.
None of the choices are correct.
Answer:
No real solutions.
Step-by-step explanation:
To solve this, we need to use Quadratic Formula.
Quadratic Formula:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]
in the form of:
[tex]a {x}^{2} + bx + c[/tex]
Given information from the question, we can deduce:
a = -1
b = -2
c = 5
Let's substitute these values into the formula.
[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]
if you punch these into the calculator.
What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, increases in value. D. As x decreases in value, decreases in value. As x increases in value, decreases in value.
The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
Which method can be used to find the end behavior of the graph?The given coordinates on the graph are;
(-3, 0), (0, 3), (2, 4), and (5, 5)
The coordinates of the starting point of the graph = (-3, 0)
Shape of the graph = Extends from point (-3, 0), upwards and to the right
Therefore;
As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.
However, given that the graph is for a square root function, the correct option is option C;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
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Find the area in square units of ABC△ plotted below.
Answer:
71
Step-by-step explanation:
Find the missing length indicated.
The missing length indicated on the right triangle is 120 units
How to determine the missing length?To start with:
The missing length in the right triangle can be represented with the variable x
Next, we have the following equivalent ratio from the given triangle
64 : x = x : 289 - 64
Express the ratio as a fraction
64/x = x/(289 - 64)
Evaluate the difference on the right-hand side
64/x = x/225
Cross multiply in the above equation
x * x = 64 * 225
This gives
x^2 = 64 * 225
Take the square root of x^2 (do not approximate)
x = 64 * 225
Take the square root of 64 and 225 (do not approximate)
x = 64 * 225
Evaluate the product of 8 and 5
x = 120
Based on the given parameters, the missing length indicated on the right triangle is 120 units
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What are the domain and range of g of x equals the square root of the quantity x plus 4?
It is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
What are the domain and range of a function?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.To find the domain and range:
The given function in the problem is: [tex]g(x)=\sqrt{x+4}[/tex]Because the square root function does not exist for negative numbers, the domain is denoted by: [tex]x+4[/tex] ≥ [tex]0[/tex] → [tex]x[/tex] ≥ [tex]-4[/tex]Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).The range of the square root function is [tex]x[/tex] ≥ [tex]0[/tex], which remains the same as there are no vertical translations.Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
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The complete question is given below:
What are the domain and range of g of x equals the square root of the quantity x plus 4?
(A) D: [4, ∞) and R: [0, ∞)
(B) D: (–4, ∞) and R: (–∞, 0)
(C) D: [–4, ∞) and R: [0, ∞)
(D) D: (4, ∞) and R: (–∞, 0)
What is equivalent to x^3y^-7
Answer: [tex]\displaystyle\\\frac{x^3}{y^7}[/tex].
Step-by-step explanation:
[tex]\displaystyle\\x^3y^{-7}=\frac{x^3}{y^7} .[/tex]
Name the rule for this sequence.
27, 21, 15, 9, 3,...
A) divide the previous term by 0.06
B) divide the previous term by 0.6
C) add 6 from the previous term
D) subtract 6 from the previous term
Answer:
D) subtract 6 from the previous term
Step-by-step explanation:
27-6=21, 21-6=15, 15-6=9, and 9-6=3
julianna wrote -16+ x = -8 on the board.Do not solve.Tell how you would simplify julianna's expression?
Answer:
x = 8
Step-by-step explanation:
→ Add 16 to both sides
x = 8
The correct solution for the given expression [tex]-16+x = -8 \\[/tex] is [tex]x[/tex] is equal to [tex]8[/tex].
Given expression:
[tex]-16+x =- 8 \\[/tex]
To solve for [tex]x[/tex], Rearrange the equation or isolate [tex]x[/tex] terms on one side of the expression.
Add [tex]8[/tex] on both side of the equation:
[tex]-16+x+8=-8+8[/tex]
Simplify:
[tex]x-8 = 0[/tex]
Isolate [tex]x[/tex] on one side:
[tex]x= 8[/tex]
The correct value of [tex]x[/tex] is [tex]8[/tex].
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1 + 7x = 5x + 25 solve for X
Answer:
x = 12
Step-by-step explanation:
1 + 7x = 5x + 25 ( subtract 5x from both sides )
1 + 2x = 25 ( subtract 1 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
Answer:
12
Step-by-step explanation:
Start by subtracting both sides by 5x:
[tex]1+7x-5x=25\\1+2x=25[/tex]
Subtract 1 from both sides
[tex]2x=24[/tex]
Divide both sides by 2
[tex]x=12[/tex]
Check[tex]1+7(12)=5(12)+25\\1+84=60+25\\85=85[/tex]
Therefore x = 12
I dont know this one
Answer:
10, 8
Step-by-step explanation:
l + w = 18
l*w = 80
8 and 10 works
Assume that thermometer readings are normally distributed with a mean of 0 C and a standard deviation of 1.00 C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)
Between 1.50 and 2.25
1. Choose the correct graph
2.the probability of getting a reading between 1.50 and 2.25
The probability of getting a reading between 1.50 and 2.25 is; 0.00546
How to find the probability from z-score?We are given the following information in the question:
Mean; μ = 0 °C
Standard Deviation; σ = 1 °C
We are given that the distribution of thermometer readings is a bell shaped distribution that is a normal distribution.
Formula for z-score is;
z = (x' - μ)/σ
P(Between 1.50 degrees and 2.25 degrees) is expressed as;
P(1.5 ≤ x ≤ 2.25)
= P((1.5 - 0)/1 ≤ z ≤ (2.25 - 0)/1))
= P(z ≤ 2.25) - P(z < 1.5)
= 0.0546 = 5.46%
The graph that correctly describes this is the first graph
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What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?
8 ft
3 ft
3 ft
Can someone help me with these two problems and show work please !!
Answer:
13. Two real solutions.
14. No real solutions.
Step-by-step explanation:
Given quadratic equations:
13. [tex]x^2+7x+10=0[/tex]
14. [tex]4x^2-3x+4=0[/tex]
[tex]{\large \textsf{Quadratic Formula: }} x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
What is the discriminant?
The discriminant (Δ) is b² - 4ac, which is under the square root in the quadratic formula. It is used to determine the number of real solutions (roots) of a quadratic:
When b² - 4ac > 0, the quadratic has two real solutions.When b² - 4ac = 0, the quadratic has one real solution.When b² - 4ac < 0, the quadratic has no real (complex) solutions.13. x² + 7x + 10 = 0
[tex]\implies a=\textsf{1},b=\textsf{7},c=\textsf{10}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta=(7)^2 - 4(1)(10)[/tex]
[tex]\implies \Delta=49 - 40[/tex]
[tex]\implies \Delta=9[/tex]
As [tex]9[/tex] > 0, this quadratic has two real solutions.
14. 4x² - 3x + 4 = 0
[tex]\implies a=\textsf{4},b=\textsf{-3},c=\textsf{4}[/tex]
Find the discriminant value.
[tex]\implies \Delta = b^2 - 4ac[/tex]
[tex]\implies \Delta = (-3)^2 - 4(4)(4)[/tex]
[tex]\implies \Delta = 9 - 64[/tex]
[tex]\implies \Delta = -55[/tex]
As [tex]-55[/tex] < 0, this quadratic has no real solutions.
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Aakash has a fever. His body temperature during the day was 99.2°F. By evening, his body temperature has increased by 3.4°F.
His body temperature in the evening is
°F.
His body temperature in the evening is 102.6 °F
How to determine his body temperature?The given parameters are:
Temperature in the morning = 99.2°F.
Temperature increase = 3.4°F.
His body temperature in the evening is calculated as:
New = Temperature in the morning + Temperature increase
So, we have
New = 99.2°F + 3.4°F
Evaluate the sum
New = 102.6 °F
Hence, his body temperature in the evening is 102.6 °F
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1. 3k − 8 = 7
2. 8b + 9 = −15
3. 8 = 3x − 13
4. 6p + 22 = 4
5. 84 = 51 + 11c
Add 8 to both sides.
3k = 7 + 8Add 7 and 8 to get 15.
3k = 15Divide both sides by 3.
k = 15 / 3Divide 15 by 3 to get 5.
k=5 ===> Answer===> Exercise 28b + 9 = −15
Subtract 9 from both sides.
8b= −15 − 9Subtract 9 from −15 to get −24.
8b = −24Divide both sides by 8.
b = -24 / 3Divide −24 entre 8 para obtener −3.
b=−3 ===> Answer===> Exercise 38 = 3x − 13
Swap the sides so that all the terms of the variables are on the left side.
3x −13 = 8Add 13 to both sides.
3x = 8 + 13Add 8 and 13 to get 21.
3x = 21Divide both sides by 3.
x = 21 / 3Divide 21 by 3 to get 7.
x = 7 ===> Answer===> Exercise 46p + 22 = 4
Subtract 22 from both sides.
6p = 4 − 22Subtract 22 from 4 to get −18.
6p = −18Divide both sides by 6.
p = -18 / 6Divide −18 entre 6 para obtener −3.
p = −3 ===> Answer===> Excercise 584 = 51 + 11c
Swap the sides so that all the terms of the variables are on the left side.
51 + 11c = 84Subtract 51 from both sides.
11c = 84 − 51Subtract 51 from 84 to get 33.
11c = 33Divide both sides by 11.
c = 33 / 11Divide 33 by 11 to get 3.
c = 3 ===> AnswerSolution 1 :-
>> 3k - 8 = 7
>> 3k = 7 + 8
>> 3k = 15
>> k = 15 / 3
>> k = 5
Solution 2 :-
>> 8b + 9 = -15
>> 8b = -15 - 9
>> 8b = -24
>> b = -24 / 8
>> b = -3
Solution 3 :-
>> 8 = 3x - 13
>> 3x = 13 + 8
>> 3x = 21
>> x = 21 / 3
>> x = 7
Solution 4 :-
>> 6p + 22 = 4
>> 6p = 4 - 22
>> 6p = -18
>> p = -18 / 6
>> p = -3
Solution 5 :-
>> 84 = 51 + 11c
>> 11c = 84 - 51
>> 11c = 33
>> c = 33 / 11
>> c = 3
6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x.
Solving a system of equations, we conclude that the value of x is 28.
How to determine the value of x?
Here we have the quadratic number pattern:
6, 15, x, 45, ...
First, we have that:
15 - 6 = 9
So 9 is the first difference.
Then we will have:
x = 15 + 9 + a
(where a is the second difference, constant of the sequence).
And:
45 = x + 9 + a + a
Then we have a system of equations:
x = 15 + 9 + a
45 = x + 9 + a + a
We can isolate a on the first equation:
a = x - 24
We can replace that in the other equation:
45 = x + 9 + 2a
45 = x + 9 + 2*(x - 24)
Now we can solve that for x:
45 - 9 = x + 2*(x - 24)
36 = 3x - 48
36 + 48 = 3x
84 = 3x
84/3 = x = 28
The value of x is 28.
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Find the value of x. Degrees in an arc!! pls help i need this to study for my test!! pls show work thank you so much :)
Considering the angle of the arc, it is found that the value of x is of x = 12º.
What is the angle of the arc?It is twice the inside angle.
In this problem, the angle of the arc is of 102º, hence the inside angle is of 51º, which means that we can solve for x as follows:
4x + 3 = 51
4x = 48
x = 12º.
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For a sample of n = 36 that has a sample variance of 1,296, what is the estimated standard error for the sample? 6 37 36 6. 9
The estimated standard error for the sample is 6
Given,
Sample size, n = 36
Sample variance, [tex]s^{2}[/tex] = 1296
Standard deviation, s = √1296
= 36
Standard error, SE = [tex]\frac{s}{\sqrt{n} }[/tex]
= [tex]\frac{36}{\sqrt{36} }[/tex]
= [tex]\frac{36}{6}[/tex]
= 6
Concept
Sample size is the number of participants or observations included in a study. It is denoted by ‘n’Sample variance is a measure of the degree to which the numbers in a list are spread out. It is denoted by '[tex]s^{2}[/tex]'Standard deviation is a measure of how dispersed the data is in relation to the mean. It is denoted by ‘s’Learn more about standard deviation here:https://brainly.com/question/13905583
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PLEASE HELP IM STUCK
Answer:
y=1
Step-by-step explanation:
Since you already found x,
We will only be needing one equation to find y..
I will take equation two: 3(2)+2y=8
Step Two: 6+2y=8 (then you minus 6 on each side)
Step Three: 2y=2 (divide)
y=1
Find the largest 4-digit number which is a perfect square.
Answer:
To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number. ∴ The biggest 4-digit number which is a perfect square = 9801.
Step-by-step explanation:
mark as brainlest answerAnswer:
9801
Step-by-step explanation:
well we know 100 squared is the first 5 digit square number so it must be 99 squared, which is 9801
math related pls help
Answer:
(a) (f +g)(x) = √(x-2) +√(x)
Step-by-step explanation:
The sum of two functions is the sum of their definitions.
Application(f +g)(x) = f(x) +g(x)
(f +g)(x) = √(x -2) +√(x)
Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.
Ujarak has 100mL t of a strong toothpaste with a 1.1% concentration of sodium fluoride. They have a weaker toothpaste with a 0.3% concentration of sodium fluoride.
What volume, in milliliters, of the weaker toothpaste would Ujarak need to add to the strong toothpaste to create a blend with a 0.8% concentration of sodium fluoride?
The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.
What are mixtures?Mixtures refers to substances which are composed of two or more substances physically combined together.
The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.
Let the volume of the 0.3 % concentration toothpaste required be x.
Final volume of toothpaste = (100 + x) mL
Amount of mixture = 0.8 * (100 + x)
100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)
solving for x
110 + 0.3x = 80 + 0.8x
110 - 80 = 0.8x - 0.3x
30 = 0.5x
x = 60
Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.
In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.
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Factor the polynomial completely
10³ -25r² - 12r + 30
An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 400min.
80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.
Find the required equation for the given question:Here in the question it is given that,
Athlete trains for 80 min each day,that is each day the athlete spends 80 min.
We have to assume the variable d the number of days the athlete spends training.Finally we have to find an equation that relates the number of days d that the athlete spends training when the athlete trains for 400 min.So we can write that,
400 min is the time spent by the athlete
400 min = number of days × time spent by the athlete in one day
400 min = d × 80
⇒ 80d = 400
Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.
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In the regular pentagon below, if AP = 4 m and BC = 10 m, find it's area.
First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)
Then find the area of one of the triangles:
Area of Triangle = [tex]\frac{1}{2} bh[/tex]
A = [tex]\frac{1}{2}[/tex] × 4 × 10
A = 20 m²
To find the area of the whole pentagon shape:
A = 20 × 5 = 100 m²
Hope it helps!
Determine the area between the curves by integrating over the x-axis or y-axis.
x=y^2
x=-|y|+12
When [tex]y\ge0[/tex] (above and on the [tex]x[/tex]-axis), we have [tex]|y|=y[/tex]. The parabola [tex]x=y^2[/tex] intersects with [tex]x=-|y|+12[/tex] in this region when
[tex]y^2 = -y + 12 \implies y^2 + y - 12 = (y-3)(y+4) = 0 \implies y=3[/tex]
On the other hand, when [tex]y<0[/tex] (below the [tex]x[/tex]-axis, we have [tex]|y|=-y[/tex], and so the curves intersect when
[tex]y^2 = -(-y) + 12 \implies y^2 - y - 12 = (y - 4)(y+3) = 0 \implies y=-3[/tex]
The area between the curves is then given by the definite integral,
[tex]\displaystyle \int_{-3}^3 (-|y| + 12) - y^2 \, dy[/tex]
The integrand is symmetric about the [tex]x[/tex]-axis, so the integral is equivalent to
[tex]\displaystyle 2\int_0^3 12 - y - y^2 \, dy = 2 \left(12y - \frac{y^2}2 - \frac{y^3}3\right)\bigg|_0^3 = \boxed{45}[/tex]
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y,z)=x2 y2 z2; 3x 4y−3z=34
The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).
An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.
A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.
predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.
By lagranier multi plur
of = hog
(2x, is, 22>= 25-47
8x=42
10x + 2 = 42
2
28
2x=4, 4= 2
=2
722 (4)
(4.9,2) = (4.2-8)
(4,2-8)= 84
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20 points and I will mark brainlyist to the first right answer.
Answer:
Step-by-step explanation:
Movie A: 267 students
Movie B: 217 students
Movie C: 233 students
Movie D: 183 students
If a card is drawn from a deck, find the probability of getting these results:
a. a 6 and a spade
b. a black king
c. a red card and a 7
d. a diamond or a heart
e. a black card
Answer:
Below in bold,
Step-by-step explanation:
a. There's is only one card that fits this description so
Probability = 1/52.
b. There are 2 black Kings so
Probability = 2/52 = 1/26.
c. There are 2 of these - 7 of diamonds and 7 of hearts
so
Probability = 2/52 = 1/26.
d. There 13 diamonds and 13 hearts so
Probability = 26/52 = 1/2.
e. There 26 black cards
Probability = 26/52 = 1/2.